The dinoflagellate genus Alexandrium is one of the major harmful algal bloom (HAB) genera with respect to the diversity, magnitude and consequences of blooms. The ability of Alexandrium to colonize multiple habitats and to persist over large regions through time is testimony to the adaptability and resilience of this group of species. Three different families of toxins, as well as an as yet incompletely characterized suite of allelochemicals are produced among Alexandrium species. Nutritional strategies are equally diverse, including the ability to utilize a range of inorganic and organic nutrient sources, and feeding by ingestion of other organisms. Many Alexandrium species have complex life histories that include sexuality and often, but not always, cyst formation, which is characteristic of a meroplanktonic life strategy and offers considerable ecological advantages. Due to the public health and ecosystem impacts of Alexandrium blooms, the genus has been extensively studied, and there exists a broad knowledge base that ranges from taxonomy and phylogeny through genomics and toxin biosynthesis to bloom dynamics and modeling. Here we present a review of the genus Alexandrium, focusing on the major toxic and otherwise harmful species.